R.C. Kar

Dynamic stability of a rectangular plate on non-homogeneous winkler foundation

Abstract The dynamic stability of a rectangular plate on non-homogeneous foundation, subjected to uniform compressive in-plane bi-axial dynamic loads and supported on completely elastically restrained boundaries is studied. The non-homogeneous foundation consists of two regions having different stiffnesses but symmetric about the centre lines of the plate. The equation governing the small amplitude motion of the system is derived by a variational method. The use of Galerkin method with reduced beam eigenfunctions transforms the system equations in matrix form. The system of coupled Mathieu-Hill equations thus obtained, are analysed by the method of multiple scales which yields the stability boundaries for different combinations of the excitation amplitude and frequency. The effects of stiffness and geometry of the foundation, boundary conditions, static load factor, in-plane load ratio and aspect ratio on the stability boundaries of the plate for first- and second-order simple and combination resonances are studied.

Parametric instability of a sandwich beam under various boundary conditions

Abstract Parametric instability of a three-layered symmetric sandwich beam subjected to a periodic axial load is considered under nine different boundary conditions. The influence of static load parameter and core-thickness parameter on the system loss factor is investigated. The effect of shear parameter on the static buckling loads is also considered, besides, the effects of shear parameter, core thickness parameter and core loss factor on the regions of parametric instability are studied.

Dynamic stability of a tapered symmetric sandwich beam

Abstract The stability of a fixed-free tapered symmetric sandwich beam under a pulsating axial force is studied. The effects of depth taper, shear parameter, core thickness and core density on the static buckling loads and the regions of parametric resonance are investigated.

Parametric instability of an elastically restrained cantilever beam

Abstract The dynamic stability of a beam elastically restrained at one end and free at the other subjected to pulsating uniaxial and follower forces has been studied. The effects of the tangency coefficient of the applied force, and the rotational and translational end-flexibilities of the beam on the regions of parametric instability of simple and combination resonances have been investigated. The results reveal that these parameters have significant influence on the dynamic stability of the system.

Stability of a nonuniform cantilever subjected to dissipative and nonconservative forces

Abstract The stability of a tapered cantilever beam subjected to a circulatory force at its free end is investigated. The effects of internal and external damping are included in the partial differential equation of motion. An adjoint variational principle has been used to determine approximately the values of the critical flutter load of the system. Graphs which demonstrate the variation of the critical nutter load with taper, damping and tangency coefficient are presented.

Parametric instability of a symmetric sandwich beam with higher order effects

The parametric instability of a pinned-pinned, three-layered symmetric sandwich beam with viscoelastic core, subjected to an axial pulsating load at one end, is considered. The analysis includes the higher order effects, viz. extensional and rotary inertias as well as bending and shear in all the layers. Numerical results are obtained with both the refined (including higher order effects) and simple (excluding these effects) analyses and the extent of applicability of the latter analysis is explored. The influence of the shear parameter upon the fundamental static buckling load as well as the effects of the relevant system parameters such as the shear, core thickness and static load parameters, the core loss factor etc., upon the regions of parametric instability are investigated. It is seen that to obtain the zones of parametric instability of short sandwich beams accurately, one must use the refined theory, since the simple theory predicts the number, as well as the locations, of the zones of instability along the frequency axis quite erroneously.

Stability of a rotating, pre-twisted, non-uniform cantilever beam with tip mass and thermal gradient subjected to a non-conservative force

Abstract The effect of thermal gradient and tangency coefficient on the stability of a pre-twisted, tapered, rotating cantilever with a tip mass and subjected to a concentrated partial follower force at the free end is investigated. The non-selfadjoint boundary value problem is formulated with the aid of a conservation law using Euler-Bernoulli theory. The associated adjoint boundary value problem is introduced and an apposite variational principle is derived. Approximate values of critical load are calculated on the basis of this variational principle and the influence of different parameters on the stability of the system is studied.

Parametric instability of a non-uniform beam with thermal gradient resting on a Pasternak foundation

Abstract The dynamic stability behaviour of a tapered cantilever beam on a Pasternak foundation under the action of a pulsating axial force and a steady, one-dimensional temperature gradient is studied. The effects of taper, elastic foundation, shear layer and thermal gradient on the natural frequencies, static buckling loads and principal regions of instability are investigated. The results reveal that increasing taper and stiffening elastic foundation have stabilizing effects, whereas increasing thermal gradient and stiffening of the shear layer have destabilizing effects on the beam.

Stability of a rotating pretwisted nonuniform cantilever with a tip mass subjected to dissipative and follower forces

Abstract The stability of a rotating pretwisted non-uniform viscoelastic cantilever beam subjected to a tangential force applied at its free end is determined by a method of approximation based on an adjoint variational principle. The coupled equations of motion are derived from a conservation law, the adjoint boundary value problem is introduced, and an approximate stability determinant is developed from the variational principle. The stability determinant is solved numerically for a variety of choices of values for the rotary inertia of the beam, transverse and rotary inertia properties of a mass capping the free end, the rotational speed, and the pretwist angle, and several graphs are presented to show the influence of these parameters upon the value of the critical flutter load.

Parametric instability of a dual-cored sandwich beam

The present paper is concerned with the study of the parametric instability of a dual-cored symmetric sandwich beam subjected to an axial pulsating load. Numerical results are obtained for various combinations of the system parameters such as the thickness, core loss-factor, shear and elastic parameters and the effects of these on the zones of parametric instability are studied.